Is there a way to mirror a mesh with hair but without deforming these?
Go to Edit Mode, flip normals on the mirrored parts, then go to Particle Mode, enable X-Mirroring, set Comb Tool strength to 0.001 and comb the original side, the mirrored sidewill match.

If there are any artifacts with some of the hair you can fix them manually or delete/recreate individual guides with mirror on.